Notice and Invitation

Oral Defense of Doctoral Dissertation
The College of Engineering and Computing, George Mason University

Christopher C. Hulbert
Bachelor of Science, Louisiana State University, 2004
Master of Science, George Mason University, 2010

Random Matrix Theory Models for Predicting Dominant Mode Rejection Beamformer Performance

Wednesday, August 17th, 2:00 - 3:00 PM EST
Room: ENGR 2901
Zoom Meeting Link: https://gmu.zoom.us/j/99674984203
Meeting ID: 996 7498 4203

All are invited to attend.

Committee
Dr. Kathleen Wage
Dr. Zhi Tian
Dr. Flavia Colonna
Dr. John Buck

Abstract
Adaptive beamformers (ABFs) use a spatial covariance matrix that is estimated from data snapshots, i.e., temporal samples from each sensor, to mitigate directional interference and attenuate uncorrelated noise. Thus, ABFs improve signal-to-interference-plus-noise ratio (SINR), an optimal criteria for many detection and estimation algorithms, over that of a
single sensor and often the conventional beamformer. SINR is a function of white noise gain (WNG), the beamformer's array gain versus spatial white noise, and interference leakage (IL), the interferer power in the beamformer output. Dominant mode rejection (DMR) is a variant of the classic minimum variance distortionless response (MVDR) algorithm that replaces the
smallest sample covariance matrix (SCM) eigenvalues by their average. By not inverting the smallest eigenvalues, DMR achieves a higher WNG than MVDR. However, DMR still suppresses the loud interferers as the largest eigenvalues are unmodified, yielding a higher SINR than MVDR.

This defense presents new analytical models of WNG and IL for the DMR ABF that are shown to match the sample mean, computed via Monte Carlo simulations, for a broad range of scenarios including with and without the signal of interest (SOI) in the training data as well as known and overestimated number of interferers. Accurate predictions for the scenarios of interest required derivation of a new random matrix theory (RMT) spiked covariance model where the number of interferers grows to infinity jointly with the SCM dimension and number of snapshots. The new RMT spiked covariance model more accurately predicts the SCM eigenspectrum, and hence the ABF metrics, when the number of snapshots is on the same
order or less than the dimension and there are a large number of interferers relative to the SCM dimension. Assuming the SOI is not in the training data and a known number of loud interferers, the analytical models show DMR achieves an average SINR loss of -3 dB when the number of snapshots is approximately twice the number of interferers, an analogous result to
the Reed-Mallett-Brennan rule for MVDR.